Is it obligatory to purchase something with money of questionable source, given that the sender of the money is young and well-off despite his family being of moderate means?

A Muslim must offer advice to their relative, especially if they are a minor and suspicion arises concerning them. Their parents should be informed so they can guide them. The money that reached you is a trust that must be fulfilled. If the relative is a minor, then pay the money to their guardian. If they are an adult of sound judgment, then dispose of it as they instructed you, or return it to them, unless they ask you for something forbidden, in which case do not cooperate with them in sin and aggression.